UVa 11178 (简单练习) Morley's Theorem

题意：

Morley定理：任意三角形中，每个角的三等分线，相交出来的三个点构成一个正三角形。

不过这和题目关系不大，题目所求是正三角形的三个点的坐标，保留6位小数。

分析：

由于对称性，求出D点，EF也是同样的。

用点和向量的形式表示一条直线，向量BA、BC的夹角为a1，则将BC逆时针旋转a1/3可求得 直线BD，同理也可求得直线CD，最后再求交点即可。

 

  1 //#define LOCAL

  2 #include <cstdio>

  3 #include <cstring>

  4 #include <algorithm>

  5 #include <cmath>

  6 using namespace std;

  7 

  8 struct Point

  9 {

 10     double x, y;

 11     Point(double x=0, double y=0) :x(x),y(y) {}

 12 };

 13 typedef Point Vector;

 14 const double EPS = 1e-10;

 15 

 16 Vector operator + (Vector A, Vector B)    { return Vector(A.x + B.x, A.y + B.y); }

 17 

 18 Vector operator - (Vector A, Vector B)    { return Vector(A.x - B.x, A.y - B.y); }

 19 

 20 Vector operator * (Vector A, double p)    { return Vector(A.x*p, A.y*p); }

 21 

 22 Vector operator / (Vector A, double p)    { return Vector(A.x/p, A.y/p); }

 23 

 24 bool operator < (const Point& a, const Point& b)

 25 { return a.x < b.x || (a.x == b.x && a.y < b.y); }

 26 

 27 int dcmp(double x)

 28 { if(fabs(x) < EPS) return 0; else x < 0 ? -1 : 1; }

 29 

 30 bool operator == (const Point& a, const Point& b)

 31 { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0; }

 32 

 33 double Dot(Vector A, Vector B)

 34 { return A.x*B.x + A.y*B.y; }

 35 

 36 double Length(Vector A)    { return sqrt(Dot(A, A)); }

 37 

 38 double Angle(Vector A, Vector B)

 39 { return acos(Dot(A, B) / Length(A) / Length(B)); }

 40 

 41 double Cross(Vector A, Vector B)

 42 { return A.x*B.y - A.y*B.x; }

 43 

 44 double Area2(Point A, Point B, Point C)

 45 { return Cross(B-A, C-A); }

 46 

 47 Vector VRotate(Vector A, double rad)

 48 {

 49     return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));

 50 }

 51 

 52 Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)

 53 {

 54     Vector u = P - Q;

 55     double t = Cross(w, u) / Cross(v, w);

 56     return P + v*t;

 57 }

 58 

 59 Point read_point(void)

 60 {

 61     double x, y;

 62     scanf("%lf%lf", &x, &y);

 63     return Point(x, y);

 64 }

 65 

 66 Point GetD(Point A, Point B, Point C)

 67 {

 68     Vector v1 = C - B;

 69     double a1 = Angle(A-B, v1);

 70     v1 = VRotate(v1, a1/3);

 71 

 72     Vector v2 = B - C;

 73     double a2 = Angle(A-C, v2);

 74     v2 = VRotate(v2, -a2/3);

 75 

 76     return GetLineIntersection(B, v1, C, v2);

 77 }

 78 

 79 int main(void)

 80 {

 81     #ifdef    LOCAL

 82         freopen("11178in.txt", "r", stdin);

 83     #endif

 84     

 85     int T;

 86     scanf("%d", &T);

 87     while(T--)

 88     {

 89         Point A, B, C, D, E, F;

 90         A = read_point();

 91         B = read_point();

 92         C = read_point();

 93         D = GetD(A, B, C);

 94         E = GetD(B, C, A);

 95         F = GetD(C, A, B);

 96         printf("%.6lf %.6lf %.6lf %.6lf %.6lf %.6lf\n", D.x, D.y, E.x, E.y, F.x, F.y);

 97     }

 98 

 99     return 0;

100 }

代码君